Well, I'm not a fan of the Kahr or S&W brand, but I have owned S&W auto's in the past and they have more of a solid feel than the Kahr. I just held a 9mm Kahr at the range today and they are compact. When dry fired, the trigger was very smooth. Actually, smoother than any small auto I've fired or owned. Priced a little high for a small concealed carry auto I thought. I doubt Kahr's customer service can match S&W. Hopefully, Kahr owners can address that issue. The smaller 9mm Sig P239 might be slightly larger than you want.

I can't think of many compact steel frame 9mms either.
The only steel frame S&Ws were full size (I think), like the 539 and 559, which aren't exactly common.
The S&W 3913 is nice (had a couple) but they have aluminum alloy frames. Nothing wrong with alum alloy frames, but since steel was specified, I guess it's out.

The Kahr K9 and MK9 have steel frames.
I had an MK9, but would advise one to get a model with the standard length (for Kahr) barrel, like the K9 or one of the Coverts (short grip, standard barrel). Reason: My MK9's slide would stop just before closed sometimes. The recoil spring on those is a dual spring arrangement, similar to Seecamps, with one spring inside the other. The thing is they both didn't exert force throughout the slide's travel. One would quit just before closed- about where mine would hang up. You could feel the force drop off when operating the slide manually. I've hand-cycled others in the gunshop, and they all felt the same way.
I've heard they've corrected this, but I don't know.
I liked the design, and gave the another shot, but went with a Covert that has the standard barrel length. It's been just fine, and rides in my front pocket .

The only other steelframed compact 9mm I can think of is the HK P7. Great gun, I think. Most people either love them or hate them. They are expensive, but used ones can sometimes be found for $800-1000- about what some "premium" 1911s run.
When I don't feel I can conceal a 1911 or HiPower well enough, I switch to my HK P7.

What about the Rohrbaugh? I don't know what their frames are made of. Anyone?

If, by chance, you meant "not plastic" instead of "steel", then that opens things up some. That brings the S&Ws back. I like the 3913, but the CS9 is a little smaller. I never had one, though, so can't say more.

The Sig P239 is another likely candidate. I had one, and liked it a lot. It had the best trigger of any Sig I've had. The Sig P225 was similar in size, but has a grip that many think is shaped better than anything. I like the P239's grip shape better, but am evidently in the minority there.